Added June 20, 2019
Taken from http://people.maths.ox.ac.uk/chengq/outreach/The%20Tricomi%20Equation.pdf
Solve for \(u(x,y)\) \[ u_{xx} + u_{yy} + \frac {\beta }{x} u_x = 0 \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] + beta/x*D[u[x,y],x] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}, Assumptions->beta>0], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,y),x$2)+ diff(u(x,y),y$2) + beta/x*diff(u(x,y),x)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build') assuming beta>0),output='realtime'));
\[u \left (x , y\right ) = \left (c_{1} \BesselJ \left (\frac {\beta }{2}-\frac {1}{2}, \sqrt {-\mathit {\_c}_{1}}\, x \right )+c_{2} \BesselY \left (\frac {\beta }{2}-\frac {1}{2}, \sqrt {-\mathit {\_c}_{1}}\, x \right )\right ) \left (c_{3} \sin \left (y \sqrt {\mathit {\_c}_{1}}\right )+c_{4} \cos \left (y \sqrt {\mathit {\_c}_{1}}\right )\right ) \sqrt {x}\, x^{-\frac {\beta }{2}}\]
____________________________________________________________________________________